Call Now to Set Up Tutoring:

(888) 888-0446

High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

Create An Account

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #31 : Intermediate Single Variable Algebra

Factor the following polynomial:

x^2-9-6xy+9y^2

Possible Answers:

(x-3y-3)(x-3y-3)

(x-3y+3)(x-3y-3)

(x-3y+3)(x+3y-3)

(x+3y+3)(x-3y-3)

(x+3y+3)(x+3y+3)

Correct answer:

(x-3y+3)(x-3y-3)

Explanation:

Begin by rearranging the terms to group together the quadratic:

x^2-9-6xy+9y^2

(x^2-6xy+9y^2)-9

Now, convert the quadratic into a square:

(x-3y)^2-9

Finally, distribute the :

(x-3y+3)(x-3y-3)

Report an Error

Example Question #11 : Factoring Polynomials

Factor the following polynomial:

m^4n+m^2n-mn^4-mn^2

Possible Answers:

mn(m-n)(m^2+mn+n^2+1)

mn(m-n)(m^2-mn+n^2+1)

mn(m-n)(m^2+mn+n^2-1)

mn(m+n)(m^2+mn+n^2+1)

mn(m-n)(m^2+mn-n^2+1)

Correct answer:

mn(m-n)(m^2+mn+n^2+1)

Explanation:

Begin by extracting from the polynomial:

m^4n+m^2n-mn^4-mn^2

mn(m^3+m-n^3-n)

Now, rearrange to combine like terms:

mn(m^3-n^3+m-n)

Extract the like terms and factor the cubic:

mn[(m-n)(m^2+mn+n^2)+1(m-n)]

Simplify by combining like terms:

mn(m-n)(m^2+mn+n^2+1)

Report an Error

Example Question #33 : Intermediate Single Variable Algebra

Factor the following polynomial:

3x^3+9x^2+9x+3

Possible Answers:

3(x-1)^2(x+1)

3(x-1)^3

3(x+1)^3

3(x+1)^2(x-1)

Correct answer:

3(x+1)^3

Explanation:

Begin by extracting from the polynomial:

3x^3+9x^2+9x+3

3(x^3+3x^2+3x+1)

Now, rearrange to combine like terms:

3(x^3+1+3x^2+3x)

Extract the like terms and factor the cubic:

3[(x+1)(x^2-x+1)+3x(x+1)]

Simplify by combining like terms:

3[(x+1)(x^2-x+1+3x)]

3(x+1)(x^2+2x+1)

3(x+1)(x+1)(x+1)

3(x+1)^3

Report an Error

Example Question #1 : Write A Polynomial Function From Its Zeros

Consider the equation $14x^{4} +Ax^{3}+Bx^{2}+Cx+6 = 0$ .

According to the Rational Zeroes Theorem, if A,B,C are all integers, then, regardless of their values, which of the following cannot be a solution to the equation?

Possible Answers:

$x = \frac{6}{7}$

x=3

$x=\frac{10}{3}$

$x=\frac{1}{2}$

$x= \frac{3}{14}$

Correct answer:

$x=\frac{10}{3}$

Explanation:

By the Rational Zeroes Theorem, any rational solution must be a factor of the constant, 6, divided by the factor of the leading coefficient, 14.

Four of the answer choices have this characteristic:

$3 = 3 \div 1$

$\frac{1}{2} = 1\div 2$

$\frac{6}{7} = 6 \div 7$

$\frac{3}{14} =3 \div14$

$\frac{10}{3}$ is in lowest terms, and 3 is not a factor of 14. It is therefore the correct answer.

Report an Error

Example Question #1 : Quadratic Equations And Inequalities

Solve the following equation using the quadratic form:

x^4-9=0

Possible Answers:

$x=\pm\sqrt{2}, \pm i\sqrt{2}$

$x=\pm\sqrt{5}, \pm i\sqrt{5}$

$x=\pm\sqrt{6}, \pm i\sqrt{6}$

$x=\pm\sqrt{4}, \pm i\sqrt{4}$

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Correct answer:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Explanation:

Factor the equation and solve:

x^4-9=0

(x^2-3)(x^2+3)=0

x^2 = 3

$x = \pm \sqrt{3}$

x^2 = -3

$x = \pm i\sqrt{3}$

Therefore there are four answers:

$x=\pm\sqrt{3}, \pm i\sqrt{3}$

Report an Error

Example Question #1 : Simplifying And Expanding Quadratic Equations

Solve the following equation using the quadratic form:

$x-4\sqrt{x}-45=0$

Possible Answers:

x=36

x=49

x=64

x=81

x=25

Correct answer:

x=81

Explanation:

Factor the equation and solve:

$x-4\sqrt{x}-45=0$

$(\sqrt{x}-9)(\sqrt{x}+5)=0$

$\sqrt{x}=9$

x=81

$\sqrt{x}=-5$

This has no solutions.

Therefore there is only one answer:

x=81

Report an Error

Example Question #1 : Understanding Quadratic Equations

Evaluate $(2x+2y)^{2}$

Possible Answers:

$4x^{2}+8xy+4y^{2}$

$\dpi{100} 4x^{2}+4xy+4y^{2}$

$\dpi{100} 2x^{2}+4xy+2y^{2}$

$\dpi{100} 4x^{2}+4y^{2}$

$\dpi{100} x^{2}+xy+y^{2}$

Correct answer:

$4x^{2}+8xy+4y^{2}$

Explanation:

In order to evaluate $\dpi{100} (2x+2y)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms.

$\dpi{100} \dpi{100} (2x+2y)^{2}=(2x+2y)(2x+2y)$

Multiply terms by way of FOIL method.

=(2x*2x)+(2x*2y)+(2y*2x)+(2y*2y)

Now multiply and simplify.

$=4x^{2}+4xy+4xy+4y^{2}$

$\rightarrow 4x^{2}+8xy+4y^{2}$

Report an Error

Example Question #2 : Understanding Quadratic Equations

Evaluate $(x-2)^{2}$

Possible Answers:

$\dpi{100} 4x^{2}-4x+4$

$\dpi{100} x^{2}-4$

$\dpi{100} x^{2}-2x+4$

$x^{2}-4x+4$

$\dpi{100} x^{2}+4$

Correct answer:

$x^{2}-4x+4$

Explanation:

In order to evaluate $\dpi{100} \dpi{100} (x-2)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

$(x-2)^{2}=(x-2)(x-2)$

Multiply terms by way of FOIL method.

=(x*x)+(x*-2)+(-2*x)+(-2*-2)

Now multiply and simplify, paying attention to signs.

$=x^{2}+(-2x)+(-2x)+4$

$\rightarrow x^{2}-4x+4$

Report an Error

Example Question #3 : Understanding Quadratic Equations

Evaluate (x+2y)*(2x-y)

Possible Answers:

$\dpi{100} x^{2}+2xy-y^{2}$

$\dpi{100} -2x^{2}-3xy+2y^{2}$

$\dpi{100} 4x^{2}+xy-4y^{2}$

$2x^{2}+3xy-2y^{2}$

$\dpi{100} 2x^{2}+4xy-2y^{2}$

Correct answer:

$2x^{2}+3xy-2y^{2}$

Explanation:

In order to evaluate (x+2y)*(2x-y) one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

Multiply terms by way of FOIL method.

=(x*2x)+(x*-y)+(2y*2x)+(2y*-y)

Now multiply and simplify, paying attention to signs.

$=2x^{2}+(-xy)+4xy+(-2y^{2})$

$\rightarrow 2x^{2}+3xy-2y^{2}$

Report an Error

Example Question #4 : Understanding Quadratic Equations

Evaluate $(x-y)^{2}$

Possible Answers:

$x^{2}-2xy+y^{2}$

$\dpi{100} 2x^{2}-4xy+2y^{2}$

$x^{2}+y^{2}$

$\dpi{100} x^{2}-y^{2}$

$\dpi{100} -x^{2}+2xy-y^{2}$

Correct answer:

$x^{2}-2xy+y^{2}$

Explanation:

In order to evaluate $\dpi{100} \dpi{100} (x-y)^{2}$ one needs to multiply the expression by itself using the laws of FOIL. In the foil method, one multiplies in the following order: first terms, outer terms, inner terms, and last terms. Be sure to pay attention to signs.

$(x-y)^{2}=(x-y)(x-y)$

Multiply terms by way of FOIL method.

=(x*x)+(x*-y)+(-y*x)+(-y*-y)

Now multiply and simplify, paying attention to signs.

$=x^{2}+(-xy)+(-xy)+(y^{2})$

$\rightarrow x^{2}-2xy+y^{2}$

Report an Error

View Tutors

Rebecca
Certified Tutor

University of South Florida, Bachelor of Science, Special Education. University of New England, Master of Science, Education.

View Tutors

Abhya
Certified Tutor

O.P JINDAL GLOBAL LAW SCHOOL, Master's/Graduate, MASTERS IN LAW.

View Tutors

Usha
Certified Tutor

SRM University, Bachelor of Technology, Biotechnology. University of Ottawa, Master of Science, Biochemistry.

All High School Math Resources

8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

ACT Tutors in Boston, LSAT Tutors in New York City, SAT Tutors in Philadelphia, LSAT Tutors in Miami, Math Tutors in Atlanta, French Tutors in Atlanta, Calculus Tutors in Dallas Fort Worth, GRE Tutors in San Diego, French Tutors in Seattle, ACT Tutors in Denver

Popular Courses & Classes

GRE Courses & Classes in Philadelphia, ACT Courses & Classes in Miami, Spanish Courses & Classes in Seattle, Spanish Courses & Classes in San Diego, ACT Courses & Classes in San Diego, MCAT Courses & Classes in Denver, GMAT Courses & Classes in Miami, SSAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Houston, ACT Courses & Classes in Boston

Popular Test Prep

MCAT Test Prep in San Francisco-Bay Area, ISEE Test Prep in Atlanta, SAT Test Prep in Atlanta, ISEE Test Prep in Denver, LSAT Test Prep in Atlanta, GRE Test Prep in Boston, MCAT Test Prep in Boston, SSAT Test Prep in Dallas Fort Worth, ACT Test Prep in Seattle, SSAT Test Prep in Washington DC

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #31 : Intermediate Single Variable Algebra

Example Question #11 : Factoring Polynomials

Example Question #33 : Intermediate Single Variable Algebra

Example Question #1 : Write A Polynomial Function From Its Zeros

Example Question #1 : Quadratic Equations And Inequalities

Example Question #1 : Simplifying And Expanding Quadratic Equations

Example Question #1 : Understanding Quadratic Equations

Example Question #2 : Understanding Quadratic Equations

Example Question #3 : Understanding Quadratic Equations

Example Question #4 : Understanding Quadratic Equations

All High School Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: